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Calc10_3day1

# Calc10_3day1 - o = 29 2 150 o =-210 o 150 o-All of the...

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10.3 day 1 Polar Coordinates Greg Kelly, Hanford High School, Richland, Washington

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One way to give someone directions is to tell them to go three blocks East and five blocks South. Another way to give directions is to point and say “Go a half mile in that direction.” Polar graphing is like the second method of giving directions. Each point is determined by a distance and an angle. θ Initial ray r A polar coordinate pair determines the location of a point. ( 29 , r θ
1 2 0 2 r π θ r a = o θ θ = (Circle centered at the origin) (Line through the origin) Some curves are easier to describe with polar coordinates:

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30 o 2 More than one coordinate pair can refer to the same point. ( 29 2,30

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Unformatted text preview: o = -( 29 2, 150 o = - -210 o 150 o-All of the polar coordinates of this point are: ( 29 ( 29 2,30 360 2, 150 360 0, 1, 2 . .. o o o o n n n + ⋅- -+ ⋅ = ± ± → Tests for Symmetry: x-axis : If (r, θ ) is on the graph, θ r 2cos r =-r so is (r, -θ ). → Tests for Symmetry: y-axis : If (r, θ ) is on the graph, θ r 2sin r = π-r so is (r, π-θ )-or (-r, -θ ). → Tests for Symmetry: origin : If (r, θ ) is on the graph, θ r π + r so is (-r, θ ) or (r, θ + π ) . tan cos r = ± → Tests for Symmetry: If a graph has two symmetries, then it has all three: ( 29 2cos 2 r θ = π...
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